Correct spelling, explanation: the word presence comes directly from an Old French word of the same spelling. There is no reason to add sc sound in the middle, so prescence is a misspelling. The correct way to spell this word is presence.

Definition of presence:
noun, a state of being present in a certain place
Your presence at this meeting is very important.
The lack of presence of the mothers at their wedding was quite sad.

Some collocations with presence:
constant presence
mere presence
strong presence
military presence

Phrases with presence:
make your presence felt/make your presence known
She certainly made her presence known at the meeting.
grace sb with presence (ironically)
Oh, look who graced us with their presence!

Incorrect spelling, explanation: prescence is a wrong form, because of the origin of presence, which is Old French presence (Modern French présence); as you can see the spelling hasn’t been changed in English. Therefore presence is the correct form.

Incorrect spelling

Incorrect spelling

Incorrect spelling

Incorrect spelling